Hirotaka Oku*, Hiroshi Takano and Masayuki ItohDepartment of Chemical Engineering and Materials Science

Faculty of Engineering, Doshisha University

Nano-Symposium 2002 : November 29th, 2002

BURSTING SUBLIMATIONBY ATOMIC SCALE SURFACE RECONSTRUCTION OF GOLD

OVERVIEWEvaporation Theory

INTRODUCTION

Sublimation is the evaporation under its melting point.

Vapor pressure under thermal equilibrium is described by Clapeyron equation.

Gas / Liquid phase boundary (Clausius - Clapeyron equation) :

m

m

VTH

dTdP

∆∆

=P : Vapor pressure, T : Temperature,ΔHm : Latent heat of phase transition,ΔVm : Change of volume at phase transitionVm(g)>Vm(l)>Vm(s), ΔVm,ΔHm>0 therefore dP/dT>0

2

lnRT

HdT

Pd vap∆=

ΔZv : Compressibity factor, (PV/RT change at normal boiling point)Antoine equation, Rankine-Dupre formula etc.

Gas / Solid phase boundary :

2

lnRTH

dTPd sub∆=

T* ,P* : Specific temperature and vapor pressureBecause ΔHsub is bigger than ΔHvap, (dlnP/dT) sub > (dlnP/dT)vap near the melting point.

P.W. Atkins : “Physical chemistry fourth edition”, pp.207-210 (Oxford university press, 1990).

OVERVIEWVapor pressure of gold

INTRODUCTION

Vapor pressure is generally a simple function of temperature.

][log][

100

1

PaPbbKT

ii −

=

9.998×10-19.996×10-1R2 [-]

1.424×1041.770×104b1 [K]

10.9710.48b0 [-]

AgAu

][/1010][ KTbbi

iPaP −=

Vapor pressure of gold is approximated by Antoine equationbetween 900 and 3000 K.

OVERVIEWSublimation Mechanism

INTRODUCTION

The position that atom most stably exists on the surface is kink, and next stable position is ledge. The most unstable position is isolation adatom on the terrace.In the sublimation process, atom moves by this order and is released from the terrace to the vacuum.The desorption speed of the adatom is given by the Polanyi-Wigner equation.

Sublimation

Therefore, the thermo energy promotes sublimation.And sublimation is mainly depend on the surface structure and properties.

( )kTEkR aX

a /exp0 −= θ

OBJECT OF THIS STUDYPhased Sublimation of Gold

OBJECT

It is known that the surface structure of gold changes by several times under its melting point.

In this study, the phased sublimation of gold is shown by the experimental data.And the mechanism of this phenomenon is considered.

The main object of this experiment is the thin-film fabrication by physical vapor deposition (PVD).In this process, pressure of chamber and temperature of gold were recorded by the computer in every one second.

When making the pressure before heating gold a standard, the rise part of pressure became the vapor pressure of gold.

EXPERIMENTAL METHODProcess of Experiment

METHOD

Evacuation :To avoid the effect of surrounding gas pressure, pre-existing gases in vacuum chamber were evacuated by a rotary pump to 3.0 Pa. After that, the pressure rises because of the inflow of helium.

Heating :The metal that was inserted in crucible was heated by the resistance heating.

Monitor :The temperature of gold was measured with an infrared thermometer.The pressure in vacuum chamber was measured with a Pirani gauge.

EXPERIMENTAL METHODConstruction of Experimental System

METHOD

Current generator

Thermal radiation thermometer

heater

exhaust

exhaust

preparation part growth part

He gas

Mass flow controller shutter

Drying column

Deoxidizing column

Pirani vacuum gauge

Temperature

Pressure

Monitor and

thermal control

Thermal control

EXPERIMENTAL METHODProblem of Measuring Instrument

METHOD

75.0

76.0

77.0

78.0

79.0

80.0

81.0

82.0

0 200 400 600 800 1000 1200 1400

Time [s]

Pressure of System [Pa]

measurement data

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200 1400

Time [s]

Temperature of Gold [℃]

measurement data The digital infrared ray radiationthermometer(Form IR-AP OCG)Precision : ~500℃ : ±3℃, 500~1000℃ : ±5℃, 1000~℃ : ±0.5%

Setting : 400~1300℃Low temperature can’t be measured.

Digital Pirani gaugeSensor : PD-3 (φ15)Range : 1.0×105~1.3×10-1PaResolution : about 1.3Pa because of quantization error.

Metal vapor by sublimation is very small.Therefore, the change of pressure can’t be measured in detail.

Spline Interpolation was adopted.

EXPERIMENTAL METHODExperimental Condition

METHOD

Initial Pressure : 25~105 Pa(Helium flow : 0.15~1.44 l/min (1atm))Most of Pressure is depend on helium flow.

Temperature of gold : 24~1150 ℃Finally, the temperature of gold reaches from 900 to 1150 ℃.

An experiment was carried out under the different temperature and pressure condition.The typical data that was gotten from the experiment is explained.Initial Pressure was 75 Pa, and the temperature of gold reached 1094 ℃.

EXPERIMENTAL RESULTInterpolation of Experimental Data

RESULT

0

200

400

600

800

1000

1200

0 200 400 600 800 1000 1200 1400

Time [s]

Temperature of Gold [℃]

interpolation

measurement data

Temperature less than 400 ℃can’ t be measured.

Heating of crucible is started at time is equal to 0s.Initial temperature is equal to room temperature.

Spline interpolation was adopted by the room temperature as data of time = 0s and measured data more than 400℃.

Interpolated

EXPERIMENTAL RESULTInterpolation of Experimental Data

RESULT

75.0

76.0

77.0

78.0

79.0

80.0

81.0

82.0

0 200 400 600 800 1000 1200 1400

Time [s]

Pressure of System [Pa]

measurement data

specified point

interpolation

Resolution of measured pressure is about 1.3Pa.

Transition pressure is only regarded as reliable data.The change of pressure is depend on the that of temperature.

Spline interpolation was adopted by the transition pressure.

Analysis of evaporation was carried out by the interpolated data.

EXPERIMENTAL RESULTEvaporation - Temperature

RESULT

75.5

76.0

76.5

77.0

77.5

78.0

78.5

79.0

79.5

80.0

0 200 400 600 800 1000 1200

Temperature [℃]

Pressure [Pa]

The sublimation promoted with the increase of the temperature.Phased pressure rise was occurred at more than 900 ℃.

EXPERIMENTAL RESULTdP/dT - Temperature

RESULT

0.0E+00

5.0E-03

1.0E-02

1.5E-02

2.0E-02

2.5E-02

3.0E-02

3.5E-02

4.0E-02

0 200 400 600 800 1000 1200

Temperature [℃]

dP/dT [Pa･K

-1]

The sublimation promoted with the increase of the temperature.The rapid pressure rise occurred at the specific temperature.The gold surface changed to the unstable state.

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

1.2E-02

0 200 400 600 800 1000 1200

Temperature [℃]

dP/dt [Pa･s-1]

EXPERIMENTAL RESULTdP/dt - Temperature

RESULT

At the specific temperature, the speed of pressure rise had a maximum.In a lot of cases, maximum was once shown at less than 900 ℃.And maximum was discretely shown at more than 900 ℃.

RESULT AND DISCUSSIONCharacteristic of Sublimation

RESULT

0.0E+00

1.0E-02

2.0E-02

3.0E-02

4.0E-02

5.0E-02

6.0E-02

7.0E-02

8.0E-02

9.0E-02

1.0E-01

0 200 400 600 800 1000 1200

Temperature [℃]

dP/dT [Pa･s-1]

10.1(2)

10.2

10.3(1)

10.3(2)

10.7

10.8

10.9

10.10(1)

10.10(2)

10.15(1)

10.15(2)

10.22(1)

10.22(2)

0.00E+00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

1.00E-02

1.20E-02

1.40E-02

1.60E-02

1.80E-02

0 200 400 600 800 1000 1200

Temperature [℃]

dP/dt [Pa･s-1]

10.1(2) 10.2

10.3(1) 10.3(2)

10.7 10.8

10.9 10.10(1)

10.10(2) 10.15(1)

10.15(2) 10.22(1)

10.22(2)

In a lot of cases, maximum was discretely shown between 400 and 900℃more than once.It considered that the phased sublimation below the melting point corresponded to the discrete change of the surface state of gold.

Phased sublimation occurred under the melting point of gold.

RESULT AND DISCUSSIONSurface Reconstruction of Gold

DISCUSSION

Equi-directionally shrunk hexagonal system~30×~30

Shrunk hexagonal system to axis direction869√3×~23

(111)

Loss of atom line6502×1(110)

Shrunk hexagonal system10205×20(001)

Characteristic of surfaceTransition temperature (K)Surface structureMiller

Index

Gold is known that indicates surface reconstruction at 650, 869 and 1020 ℃.Because sublimation depends on the state of surface, phased sublimation is considered that based on surface reconstruction of gold.

Au(001)5×20 Au(110)2×1

RESULT AND DISCUSSIONRoughening transition

DISCUSSION

The phase transition that roughness of solid surface increases at high temperature (under melting point) is called roughening transition.If roughening transition occurred, the number of atom that exist on terrace increases and sublimation easily occurs.

Surface reconstruction and roughening transition are thought as the main reason of phased sublimation.

Sublimation

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0 20 40 60 80 100 120

Initial Pressure [Pa]

Vapor Pressure of Gold [Pa]

T<1000℃

T=1000-1050℃

T=1050-1100℃

T>1100℃

EXPERIMENTAL RESULTEvaporation – Helium Flow Rate

RESULT

The helium flow blows gold vapor !

Vapor pressure of gold increased with increasing helium flow.

The helium flow has the effect to diffuse gold vapor into the vacuum chamber without making gold vapor cohere regardless of the temperature.

When making the pressure before gold evaporates a standard, the difference of pressure becomes the vapor pressure of gold.

Pirani gaugePirani gauge

EXPERIMENTAL RESULTEvaporation – Final Temperature

RESULT

High saturation ratio rapidly promotes particle growth and the number density of gold particles decreases consequently.As for the robbed heat per particle, the independent atoms are bigger than the cluster.

Low saturation ratio High saturation ratio

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

900 950 1000 1050 1100 1150 1200

Final Temperature [℃]

Vapor Pressure of Gold [Pa]

<50Pa

50-60Pa

60-70Pa

70-80Pa

80-90Pa

90-100Pa

>100Pa

Vapor pressure of gold decreased with heating gold.The pirani gauge measures pressure from the heat that was robbed from heated solid by the crash of cold gas particles.Heating gold promotes sublimation and increases saturation ratio.At the same time, number density of gold particles rapidly decreases and the measured pressure that is correspond to robbed heat will decrease.

RESULT AND DISCUSSIONEffect of helium flow and temperature

DISCUSSION

It was confirmed that the vapor pressure of gold is affected by parameters such as the helium flow rate and saturation ratio.

To control the particle size accurately, not only temperature of gold but also these parameter should be considered.

Helium flow rate :The helium flow has the effect to diffuse gold vapor into the vacuum chamber without making gold vapor cohere.

Saturation ratio of gold :Heating gold promotes sublimation and increases saturation ratio.The large particles grew and the number density of gold will decrease.

CONCLUSIONThe Knowledge Obtained by This Research

CONCLUSION

Experimental Result :In a lot of cases, maximum of sublimation speed was discretely shown between 400 and 900℃ more than once.

Consideration :Surface reconstruction and roughening transition are thought as the main reason of phased sublimation.

Suggestion :In case of the sublimation, it is difficult to show vapor pressure as the function with simple temperature.The vapor pressure of crystallized materials under the temperature less than melting point should be reconsidered from the viewpoint of the atomic scale reconstruction process of surface.

BACKGROUNDQuantum Dot Physical Deposition (QDPD) Process

THEORY

Nano-sized particle

SubstrateSubstrate

... .... ...

Substrate

Evaporation Nucleation

Deposition Metal island Thin-film Fabrication

Pressure condition affects particle size.

(1) 実験系圧力条件の検討(1.2) 実験系の圧力条件について

Result

・ 真空容器の物質収支を立てて、系をモデル化した。

［容器内圧力上昇要因］① SHe：ヘリウムガスの流入② ｖmetal：ルツボからの金属蒸気蒸発③ Qv：真空容器からの気体放出④ Ql：リーク

［圧力減少要因］⑤ S：ポンプによる排気

( ) ( ){ }lvmetalHe QQvSPPSdtdPV +++−=−

中・高真空領域（102～10-5Pa）では、dP/dtが無視できるので、

( ) ( )metalHe

lv

vSSQQtP+−+

=

Experimental ParameterThe pressure condition of the experiment system

Result

・It calculated pressure rise speed as the summation between the gas slip speedand the leak speed by build-up method.

13210050.1 −− ⋅⋅×=+=∴ smPaQQQ lv

y = 1.050E-02x - 1.808E+00

R2 = 9.994E-01

0.00E+00

1.00E+01

2.00E+01

3.00E+01

4.00E+01

5.00E+01

6.00E+01

7.00E+01

0 1000 2000 3000 4000 5000 6000

Time [s]

Pressure [Pa・m3]

Because the reaching pressure is equal to the research in the past, the leak speed is the inside of the latitude.

(3) 実験系を反映した粒子密度の設定(3.1) 蒸発速度

Result

蒸気圧Pのとき、単位時間、単位面積あたりの入射分子数は、

mkTpjcoll π2

=

入射して、固相に凝集する分子数は、凝集係数αとすると、

mkTpjj collin π

αα2

==

固気界面では、平衡蒸気圧P0で平衡状態が成立するので、実測した蒸発速度jvと凝集速度jinは等しい。

eqcoll

eqv jj /=α

凝集係数αは、過飽和度、面方位、表面形態に依存する。値は、温度と共に増加し、溶融状態でほぼ1になる。

外部の蒸気圧をP、温度をToutとすると、固相分子数Ncの時間変化は、下式のようになる。

mkTpjjj eq

colleqin

eqv π

αα2

0===

凝集係数αは右式により定義できる。

mkTp

mkTpjj

dtdN

out

eqvin

c

πα

πα

220−=−=

> 固相分子数Ncの時間変化から、飛び出す金原子の個数を計算できる。

(3) 実験系を反映した粒子密度の設定(3.2) 計測結果（圧力）

Result

① ロータリーポンプによる排気（Pe=3Pa）② ディフュージョンポンプによる排気（Pe=0.2Pa）③ メカニカルブースターポンプ始動　 ヘリウム流す　 (流量、シャッターの閉め具合で圧力調整可能　　流出と同時に大量のヘリウムが放出され圧力上昇)

5.50E+01

6.50E+01

7.50E+01

8.50E+01

9.50E+01

1.05E+02

1.15E+02

0 200 400 600 800 1000 1200 1400 1600

Time [s]

Pressure [Pa]

9/3(1)M

9/3(2)M

0.00E+00

2.00E+01

4.00E+01

6.00E+01

8.00E+01

1.00E+02

1.20E+02

1.40E+02

0 500 1000 1500 2000 2500

Time [s]

Pressure [Pa]

9/3(0)S

9/3(1)S

9/3(2)S

真空引き－ヘリウム流す

① 電力送信開始　 段階的に金原子の蒸発により圧力は上昇する② シャッター開放　 系の体積増加に加えメカニカルブースターポンプ　 の排気が有効になり、圧力は減少　 基板への沈着③ シャッター閉める　 急激な圧力上昇

電力送信－粒子生成

① ② ③

① ②

③

(2) 熱電対によるルツボ温度の計測(2.2) 有限要素法によるルツボ温度分布の解析

Result

先端接触方式により求められた温度から、ルツボの断面を要素分割し、有限要素法により温度分布の解析をおこなった。

タングステンバスケットヒーターを800℃と仮定し、熱伝導率はアルミナの値3.6×104W/m･Kを適用した。先端接触方式により求められた温度を境界条件として指定し、解くと左図の結果が得られた。

タングステンヒーターが密に存在するルツボ下部では温度が高くなっていることが分かる。

> しかし、計測された温度に信頼性がないため、結果として求められた温度分布にも信頼性がない。

0

0.4

0.8

1.2

1.62

2.4

2.8

3.2

3.64

4.4

4.8

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

0

X [mm]

Y [mm]

700-800

600-700

500-600

400-500

300-400

200-300

100-200

0-100

Experimental MethodInfrared thermometer

Caution

It is made in Inc. CHINO the Infrared thermometer for the middle and high temperature in IR-A series. The digital infrared ray radiation thermometer (Form IR-AP OCG RANGE : 300-900℃)The distance coefficient: 50, the detection device: Ge (The measurement wavelength of 1.6μm)Precision : ~500℃ : ±3℃, 500~1000℃ : ±5℃, 1000~℃ : ±0.5%

①When the detection device is Ge, 300~1500℃ become a measurement range. However, because 900℃ become the upper limit on the specification, at higher temperature, there is no guarantee of the precision.> Thermocouple ?② It considers the diameter of the crucible (0.8cm) and the light axis must be correctly adjusted.> OK !③ The emissivity of gold is 0.14 (solid) and 0.22 (liquid).> It is revised in the program.

The measurement diameter = measurement distance(53cm) / distance coefficient(50) = 1.06cm

(1) The simultaneous measurement(1.1) The measurement model

Result

The simultaneous measurement of the thermocouple and the infrared thermometer:

<The measurement point>・thermocouple was installed between the crucible wall and gold. The thermocouple measured the temperature of the wall part.・The infrared thermometer measured a surface of the gold.

<The advantage>The condition of gold can be more precisely known in measuring the temperature of surface and wall part and analyzing the pressure change.

Because the temperature of the wall part wasn't influenced by the cooling by helium, relation between the sending electric power and the temperature of gold can be fixed.

10.22(1)

0

200

400

600

800

1000

1200

1400

0 500 1000 1500 2000

Time [s]

Temperature [℃]

Thermo couple

Infrared thermometer

(1) The simultaneous measurement(1.2) Result (1) : Temperature and nAu

Result

0

5E+17

1E+18

1.5E+18

2E+18

2.5E+18

3E+18

3.5E+18

0 500 1000 1500 2000

Time [s]

nAu

The temperature of the wall part decreased within 1300-1600 s. As for the surface temperature, it continued to rise.The evaporative quantity of gold was decreased within 1300-1600 s and depended on the wall temperature.

At this time, the energy that is used for the temperature of gold rise seems to lose as the vaporization heat in addition to the latent heat that accompanies phase transition.

When gold liquefied, the temperature inclination occurred between the wall part and the surface again.

0

200

400

600

800

1000

1200

1400

0 200 400 600 800 1000 1200 1400

Time [s]

Temperature [℃]

Thermo couple

Infrared thernometer

(1) The simultaneous measurement(1.2) Result (2) : Temperature and nAu

Result

The wall temperature temporarily decreased within 900-1050 s.Then the surface temperature is rising but that the wall temperature is constant.

At this time, The energy that is used for the temperature of gold rise seemed to be consumed as the latent heat.

Even if the inside of gold made phase transition, the evaporative quantity didn't rise immediately.

0.00E+00

1.00E+18

2.00E+18

3.00E+18

4.00E+18

5.00E+18

6.00E+18

7.00E+18

8.00E+18

9.00E+18

1.00E+19

0 200 400 600 800 1000 1200 1400

Time [s]

nAu

10.22(1)

0

200

400

600

800

1000

1200

1400

0 500 1000 1500 2000

Time [s]

Temperature [℃]

Thermo couple

Infrared thermometer

(1) The simultaneous measurement(1.3) Temperature and the state of gold

Result

Early stage(solid)

During phase transition(solid & liquid)

After the melting(liquid)

In case of phase transition, the energy loss was occurred by the latent heat and the temperature difference between the wall and the surface decreased.

(1) The simultaneous measurement(1.4) Temperature difference

Result

The temporary decrease of temperature was occurred under the condition, that the surface temperature is rising but that the wall temperature is constant.The melting point can be judged as about 1050 ℃ from the minimal value of the temperature difference.

-6.00E+01

-4.00E+01

-2.00E+01

0.00E+00

2.00E+01

4.00E+01

6.00E+01

8.00E+01

1.00E+02

100 300 500 700 900 1100 1300 1500 1700 1900

Time [s]

T(T.couple) - T(Inf.Thermo.) [K]

10.22(1)

10.22(2)

(1) The simultaneous measurement(1.5) Power and wall temperature

Result

y = 9.4628x + 446.91

R2 = 0.9907

y = 8.8571x + 424.29

R2 = 0.9924

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100

Power [J/s]

Temperature (T.couple) [℃]

10/22(1)

10/22(2)

線形 (10/22(2))

線形 (10/22(1))

The sending electric power and the wall temperature were approximately proportional in the range of P=45-85J･s-1.

Fundamental DataSurface reconstruction

Data

Equi-directionally shrunk hexagonal system-~30×~30(111)

Shrunk hexagonal system to axis direction869√3×~23(111)

Loss of atomic line6502×1(110)

Shrunk hexagonal system10205×20(001)

Au

Loss of atomic line-2×1(110)

Shrunk and rotated hexagonal system1840(14 1)(-1 5)

(001)Pt

Shrunk hexagonal system to axis direction8005×1(001)Ir

-

-

200

Transition temperature (K)

Loss of atomic line2×1(110)

Atomic transition in surfacenon-coordination(001)Mo

Atomic transition in surface√2×√2(001)W

Characteristic of surfaceSurface structure

Miller Indexmetal

(3) The control algorithm(3.1) Relationship of the experiment parameters

Overview

TEM observation

: Control object : monitoring parameter (dynamic change)

: Control parameter : Setting Parameter (constant)

Electric current

EvaporationTemperature

Particlediameter,

S.deviationHelium

flow rate

Setting of equipment

Deposition time

It influences directly.

(3) The control algorithm(3.2) Power control : past

Overview

Electric current

EvaporationParticlediameter,

S.deviation

Temperature

Electric power was controlled by PID control.In this way, the temperature and evaporative quantity are not directly controlled.Therefore, the evaporative quantity that mostly related to the property of particlewasn't kept constant.

Electric power

Voltage

(3) The control algorithm(3.2) Evaporation control : future

Overview

Electric current

EvaporationParticlediameter,

S.deviationPID control.

Temperature

To keep evaporative quantity constant,temperature of gold is controlled by PID control.It must be more simple and effective control !

Keep constant

evaporation !

Feedback.